L-凸空间的一个极大极小不等式及应用

A minimax inequality in L-convex spaces and it application

运用L-凸空间中的一个极大极小不等式,对L-凸空间中的抽象变分不等式和似变分不等式解的存在性,Ky Fan型截口定理,以及具有扰动的二人零和博弈和多人非合作博弈均衡的存在性进行研究,从而得到没有线性结构的L-凸空间中一些新的抽象变分不等式和似变分不等式解的存在性结果和一个Ky Fan型截口定理.最后得到了一个具有扰动的二人零和博弈和一个多人非合作博弈的均衡存在性结果.计算结果与其他相关结果相比,条件是比较弱的.

By using a minimax inequality in L-convex spaces, an analysis is made on the existence of the solutions to abstract variational inequality and variational-like inequality, the Ky Fan section theorem, and the equilibrium existence of perturbed zero-sum game for two persons and non-cooperative game for multiple players in L-convex spaces. As a conclusion, some new results about the existence of the solutions to abstract Variational inequality and variational-like inequality and a Ky Fan section theorem in L-convex spaces without linear structure are drawn, and the result of the equilibrium existence of perturbed zero-sum game for two persons and non-cooperative game for multiple players are finally obtained. The conditions of the results in this paper are weak as compared with those in other literatures.